Question

Currents I1, I2 and I3 meet at a junction in a circuit. All currents are marked as entering the node. If I1 = -6sin(ωt) mA and I2 = 8 cos(ωt) mA, the I3 is ________ (a) 10 cos(ωt + 36.87) mA (b) 14 cos(ωt + 36.87) mA (c) -14 sin(ωt + 36.87) mA (d) -10 cos(ωt + 36.87) mA I got this question in an interview for job. Query is from Advanced Problems on Network Theory topic in chapter Network Theory and Complex Circuit Diagram of Network Theory Select the correct answer from above options network theory questions and answers, network theory questions pdf, network theory question bank, network theory gate questions and answers pdf, mcq on network theory pdf, gate network theory questions and solutions, network theory mcq Test , ies network theory questions, Network theory Questions for GATE EC Exam, Network Theory MCQ (Multiple Choice Questions)

Answer 1

Correct choice is (d) -10 cos(ωt + 36.87) mA To explain I would say: Applying KCL, we get, I1 + I2 + I3 = 0 ∴ -6 sin(ωt) + 8 cos(ωt) + I3 = 0 ∴ I3 = 6 sin (ωt) – 8 cos (ωt) = 10[sin (ωt).sin (36.86) – cos (ωt) cos (36.86)] =-10[cos (ωt) cos (36.86) – sin (ωt) sin (36.86)] = -10 cos (ωt + 36.86) [As, cos (A+B) = cosA.cosB – sinA.sinB].